Two-hadron saturation for the pseudoscalar-vector-vector correlator and phenomenological applications
Abstrakt
The pseudoscalar-vector-vector correlator is constructedusingtwomesonmultipletsinthevectorandtwo in the pseudoscalar channel. The parameters are constrained bytheoperatorproductexpansionatleadingorderwheretwo or all three momenta are considered as large.
Demanding in addition the Brodsky-Lepage limit one obtains (in the chiral limit) a pion-vector-vector (πVV) correlator with only one free parameter. The singly virtual pion transition form factor Fπ0γγASTERISK OPERATOR and the decay width of ω RIGHTWARDS ARROW π0γ are independent of this parameter and can serve as cross-checks of theresults.Thefreeparameterisdeterminedfromafitofthe ω-π transition form factorFπ0ωγASTERISK OPERATOR.
The resulting πVV correlator is used to calculate the decay widths ω RIGHTWARDS ARROW π0e+eMINUS SIGN and ω RIGHTWARDS ARROW π0μ+μMINUS SIGN and finally the widths of the rare decay π0 RIGHTWARDS ARROW e+eMINUS SIGN and of the Dalitz decay π0 RIGHTWARDS ARROW e+eMINUS SIGN γ. Incorporating radiative QED corrections the calculations of π0 decays are compared to the KTeV results.
We find a deviation of 2 σ or less for the rare pion decay.